Non-Local Rheology of Intermediate Granular Flows

Publication Reference: 
ARR-12-02
Author Last Name: 
Daniels
Authors: 
Karen E. Daniels
Report Type: 
ARR
Research Area: 
Powder Flow
Publication Year: 
2017
Publication Month: 
12
Country: 
United States

EXECUTIVE  SUMMARY

Currently, there is no first-principles, general theory of intermediate dry granular flow that predicts its rheological response as a function of particle size, shape, and friction (even leaving aside adhesion, which is more challenging still). It is an open question what constitutive equations best describe such flows. Therefore, there is a need for experimental data which tests these theories, and thereby provides an improved understanding of how particle properties control the rheology of granular materials, independent of the flow geometry. Rather than using empirical relations fit to bulk data for a particular flow geometry and particles, we aim to connect grain-scale parameters to macroscale behaviors.

In this second year of effort, we have have continued our laboratory testing of one nonlocal theory [cooperative model, Kamrin and Koval 2012], and added a comparison to a second model [gradient model, Bouzid et al. 2013]. To test the efficacy of these two models across different packing fractions and shear rates, we performed experiments in a quasi-2D annular shear cell with a fixed outer wall and a rotating inner wall, using photoelastic particles. The apparatus is designed to measure both the stress ratio µ (the ratio of shear to normal stress) and the inertial number I through the use of a torque sensor, laser-cut leaf springs, and particle-tracking. We obtain

µ(I) curves for several different packing fractions and rotation rates, and successfully find that a single set of model parameters is able to capture the full range of data collected once we account for frictional drag with the bottom plate.   Our measurements confirm the prediction that there    is growing lengthscale at a finite value µs, associated with a frictional yield criterion. Finally, we newly identify the physical mechanism behind this transition at µs by observing that it corresponds to a drop in the susceptibility to force chain fluctuations.

We have begun experiments testing the influence of other particle-properties, starting with particle material and shape. Our preliminary investigations have revealed that the shape of the interparticle contacts (rounded vs. angular) is an important control on µs, separate from material properties such as the coefficient of friction or elastic modulus. In addition, we observe that the model parameters will require adjustment in order to fit µ(I) and velocity profile data collected for different particle types, as expected.